Sign detection in multi-dimensional signal measurements

ABSTRACT

Systems, methods, circuits and computer-readable mediums are disclosed for sign detection in multi-dimensional signal measurements. In some implementations, orthogonally oriented antennas are configured to generate signals in response to a magnetic field, where the signals correspond to components of magnetic field vectors in space. A circuit is coupled to the antennas and configured to: determine polarities of the signals based on phase measurements between the signals; reduce a possible number of magnetic field vector interpretations based on the determined polarities of the signals; reduce a possible number of angles or angle differences between the magnetic field vectors based on the reduced possible number of magnetic field vector interpretations; compare the reduced possible number of angles or angle differences to predetermined angle or angle differences; and detect a relay attack based on results of the comparing.

CLAIM OF PRIORITY

This application is a continuation of and claims priority to U.S. patentapplication Ser. No. 14/560,713, filed Dec. 4, 2014, which claimspriority to U.S. Provisional Application Ser. No. 62/084,517, filed onNov. 25, 2014, the entire contents of each of which are herebyincorporated by reference.

TECHNICAL FIELD

This disclosure relates generally to multi-dimensional signalmeasurements.

BACKGROUND

Contactless data communication has been employed in multiple industries,including the automotive industry. There, contactless data communicationis used to gain access to a vehicle. A key or key fob is held by aperson and is operable to communicate with a vehicle when the key fob iswithin range of wireless communication with the vehicle. The person maypress a button on the vehicle or lift the handle of a door of thevehicle to initiate communication between the vehicle and the key or keyfob. Once communication is initiated, the vehicle and the key or key fobmay exchange messages to allow the person access to the vehicle. Forexample, the key or key fob may transmit one or more authenticationmessages that the vehicle validates.

One problem that has arisen with contactless data communication is thatit is susceptible to a relay attack. In the context of access tovehicles, this attack includes a person initiating the communicationwith the vehicle by pushing a button on the vehicle or lifting a handleon the vehicle's door. The vehicle then transmits a signal, which iscaptured by the person and relayed to a remote device using atransceiver. The remote device may be located away from the vehicle butin proximity to the key or key fob. For example, the vehicle may be in aparking lot of a restaurant and the owner of the vehicle may be in therestaurant. The remote device may be located inside the restaurant andmay relay the signal transmitted by the vehicle in the restaurant. Thekey fob, while in the possession of the owner, may receive the signaltransmitted by the vehicle as a result of the remote device and mayrespond with authentication signals. The remote device may capture theauthentication signals and transmit them to the person in proximity withthe vehicle who initiated the communication. The transceiver held by theperson may transmit the authentication signals to the vehicle and thevehicle may validate the authentication signals. This may allow anunauthorized person access to the vehicle.

SUMMARY

Systems, methods, circuits and computer-readable mediums are disclosedfor sign detection in multi-dimensional signal measurements.

In some implementations, a system includes orthogonally orientedantennas that are configured to generate signals in response to amagnetic field, where the signals correspond to components of magneticfield vectors in space. A circuit is coupled to the antennas andconfigured to: determine polarities of the signals based on phasemeasurements between the signals; reduce a possible number of magneticfield vector interpretations based on the determined polarities of thesignals; reduce a possible number of angles or angle differences betweenthe magnetic field vectors based on the reduced possible number ofmagnetic field vector interpretations; compare the reduced possiblenumber of angles or angle differences to predetermined angle or angledifferences; and detect a relay attack based on results of thecomparing.

In some implementations, a method comprises: generating, by orthogonallyoriented antennas of a system, signals in response to a magnetic field,where the signals correspond to components of magnetic field vectors inspace; determining, by a circuit of the system, polarities of thesignals based on phase measurements between the signals; reducing, bythe circuit, a possible number of magnetic field vector interpretationsbased on the determined polarities of the signals; reducing, by thecircuit, a possible number of angles or angle differences between themagnetic field vectors based on the reduced possible number of magneticfield vector interpretations; comparing, by the circuit, the reducedpossible number of angles or angle differences to predetermined angle orangle differences; and detecting, by the circuit, a relay attack basedon results of the comparing.

In some implementations, a non-transitory, computer-readable storagemedium includes instructions, which when executed by one or moreprocessors, causes the one or more processors to perform operationscomprising: generating, by orthogonally oriented antennas of a system,signals in response to a magnetic field, where the signals correspond tocomponents of magnetic field vectors in space; determining, by a circuitof the system, polarities of the signals based on phase measurementsbetween the signals; reducing, by the circuit, a possible number ofmagnetic field vector interpretations based on the determined polaritiesof the signals; reducing a possible number of angles or angledifferences between the magnetic field vectors based on the reducedpossible number of magnetic vector interpretations; comparing thereduced possible number of angles or angle differences to predeterminedangles or angle differences; and detecting a relay attack based onresults of the comparing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates comparing channel input signals to determine phaserelationships between the channel input signals.

FIGS. 2A and 2B illustrate an example in-phase relationship betweencomparator output signals for x and y channels and an exampleout-of-phase relationship between comparator output signals for x and zchannels, respectively.

FIG. 3 illustrates a hardware system including comparators for detectingphase (sign) information between two channels according to someembodiments.

FIG. 4 is a conceptual block diagram illustrating components used in asystem for secure contactless data communication that implements signdetection in multi-dimensional signal measurements according to someembodiments.

FIG. 5 is a flow diagram of a process of sign detection inmulti-dimensional signal measurements.

DETAILED DESCRIPTION

One type of contactless data communication for vehicles is the passiveentry, passive start (PEPS) system. The PEPS system uses several lowfrequency (LF) antennas within a vehicle that are operated sequentiallytogether with a key or key fob incorporating a three-dimensional (3D)magnetic antenna to detect a transmitted magnetic field from the LFvehicle antennas. The key or key fob includes an LF receiver thatprovides three communication channels to receive the 3 orientations (x,y, z) of a magnetic field transmitted by the LF vehicle antennas. Thethree communication channels provide voltages that can be measured andused to calculate a received signal strength indicator (RSSI).

The measured channel voltages (x, y, z) represent a vector per eachtransmitting vehicle antenna having an amplitude and an orientationwithin a 3D space, where the amplitude is given byAmplitude=√{square root over (x ² +y ² +z ²)}.  [1]

To avoid the relay attack scenario described above, the angles betweenthe vectors can be calculated. Indeed, an embodiment provides thatangles between vectors can be used for defending against relay attacksfor two antennas that are operated sequentially or at the same time.When two vehicle antennas are operated sequentially, two individualtriples (x, y, z) of voltages can be measured sequentially from the LFreceiver channels, representing the two vectors generated by the two carantennas.

As an example, assume that two vectors

and

are measured, having components (1, 4, −2) and (−3, 3, 1), respectively.The amplitudes of these vectors can be calculated:Amplitude_(a)=√{square root over (1²+4²+−2²=4.58)}Amplitude_(b)=√{square root over (−3²+3²+−1²=4.36)}

The angle between the two vectors can be calculated by the followingformula:

$\begin{matrix}{\theta = {{\cos^{- 1}\frac{\overset{\rightharpoonup}{a} \cdot \overset{\rightharpoonup}{b}}{{\overset{\rightharpoonup}{a}}{\overset{\rightharpoonup}{b}}}} = {69.49{{^\circ}.}}}} & \lbrack 2\rbrack\end{matrix}$

As can be seen in this example, the individual vector components (x, y,z) can have different polarities according to the orientation and theposition of the receiving 3D antenna (e.g., key or key fob) and thetransmitting vehicle antenna. Receivers that are in the market today donot measure the polarity of the channel voltages. For example, there canbe eight possible interpretations of the measured vector components (x,y, z). In the above example, vector

could be interpreted as: (1, 4, 2), (1, 4, −2), (1, −4, 2), (1, −4, −2),(−1, 4, 2), (−1, 4, −2), (−1, −4, 2) and (−1, −4, −2). The eightinterpretations of vector

could be interpreted as: (3, 3, 1), (3, 3, −1), (3, −3, 1), (3, −3, −1),(−3, 3, 1), (−3, 3, −1), (−3, −3, 1) and (−3, −3, −1). The resultingvector amplitudes are not affected by the multiple interpretations bythe term

·

. The resulting calculations will result in 8*8=64 differentinterpretations where some of these are equal. For the vectors

and

in the above example,

·

results in the following 64 values:

7 11 −17 −13 13 17 −11 −7 11 7 −13 −17 17 13 −7 −11 −17 −13 7 11 −11 −713 17 −13 −17 11 7 −7 −11 17 13 13 17 −11 −7 7 11 −17 −13 17 13 −7 −1111 7 −13 −17 −11 −7 13 17 −17 −13 7 11 −7 −11 17 13 −13 −17 11 7

Due to the chosen example, many of the samples are equal, but even inthis case eight different values are possible: (7, −7, 11, −11, 13, −13,17, −17). This results in 64 calculated angles.

69.5 56.6 148.3 130.6 49.4 31.7 123.4 110.5 56.6 69.5 130.6 148.3 31.749.4 110.5 123.4 148.3 130.6 69.5 56.6 123.4 110.5 49.4 31.7 130.6 148.356.6 69.5 110.5 123.4 31.7 49.4 49.4 31.7 123.4 110.5 69.5 56.6 148.3130.6 31.7 49.4 110.5 123.4 56.6 69.5 130.6 148.3 123.4 110.5 49.4 31.7148.3 130.6 69.5 56.6 110.5 123.4 31.7 49.4 130.6 148.3 56.6 69.5

Out of the 64 angles possible angles there are eight different angles:(69.5, 56.6, 148.3, 130.6, 49.4, 31.7, 123.4, 110.5). Due to the varietyof angle interpretations and taking some measurement tolerances intoaccount it is not reliably possible to use the calculated angle forrelay attack purposes. As can be observed by the above example, it isdesirable to greatly reduce the number of possible angleinterpretations. As described in detail below, the number of possibleangle interpretations can be reduced by measuring the polarity of theindividual vector components (x, y, z).

FIG. 1 illustrates comparing channel input signals to determine phaserelationships between the channel input signals. In someimplementations, a comparator function (implemented in software orhardware) can be used to detect if the x, y, z channel voltage values(sine waves) are above certain threshold values.

Referring to FIG. 1, a diagram 100 is shown with three signals. Signal101 shows the input signal of an individual channel (x, y, z). Signal102 represents the threshold signal of the comparator. Signal 103represents the output of the comparator.

To detect the polarity between two individual channels (x, y or x, z ory, z), the comparator output signals (comp_out) of two individualchannels are combined by an AND function. If comp_out_x AND comp_out_yis TRUE at any time, y is in phase with x. If comp_out_x AND comp_out_zis TRUE at any time, z is in phase with x. If comp_out_y AND comp_out_zis TRUE at any time, z is in phase with y.

FIGS. 2A and 2B illustrate an example in-phase relationship betweencomparator output signals for x and y channels and an exampleout-of-phase relationship between comparator output signals for x and zchannels, respectively.

FIG. 2A shows the input voltage signals on the x and y channels, thecomparator output signals for the x and y channels and the output of anAND function applied to the comparator output signals. When inputsignals 201, 202 of the x and y channels exceed their respectivecomparator threshold values 206, 207, comparator output signals 203, 204are generated and applied as inputs to an AND function (e.g., an ANDgate). In this example, comparator output signals 203, 204 are high atthe same time and the AND function generates output 205, which indicatesan in-phase relationship between the x and y channels.

FIG. 2B shows the input voltage signals on the x and z channels, thecomparator output signals for the x and z channels and the output of anAND function applied to the comparator output signals for the x and zchannels. When input signals 208, 209 of the x and z channels exceedtheir respective comparator threshold values 212, 213, comparator outputsignals 210, 211 are generated and applied as inputs to an AND function(e.g., an AND gate). In this example, comparator output signals 210, 211are not high at the same time and the AND function does not generate anoutput, which indicates an out-of-phase relationship between the x and zchannels.

It can be observed from the examples shown in FIGS. 2A and 2B that thereis usually some phase tolerance for in-phase channels (FIG. 2A) andopposite polarity channels (FIG. 2B), which will influence the selectionof the comparator threshold value. To ensure that in-phase channels aredetected securely, the comparator value should be low. To prevent thatchannels with opposite polarity are falsely recognized as “in phase” thecomparator value should be high. In some implementations, an optimumcompromise is to set the comparator threshold value where it is exceededby 50% of the time during the positive half wave (90°). Thus, thecomparator threshold value can be set to

$\frac{V_{peak}}{\sqrt{2}}$or 70.7% of the peak voltage value of the channel. If the comparatorthreshold value is set exactly to 70.7% of the peak value, the maximumallowed channel phase shift would be 90° to be recognized as being inphase. Tolerances of the implementation (e.g., comparator thresholds)and the RSSI measurement values (e.g., measured x, y, z components inthe receiving antenna) are not considered here for explanation of theprincipal.

In some implementations, the polarity information can be used to improvethe evaluation of the measured vector components (x, y, z) that aremeasured from several antennas (Ax, Ay, Az). For example, angle and/orangle difference determination between vectors resulting from differentvehicle transmit antennas can be calculated. In some implementations,ratios between the same vector component measurements from differentvehicle transmit antennas can be determined, such as Vx/A1/VxA2,VyA1/VyA2, VzA1/Vz2, where A1, A2 are two different vehicle transmitantennas. In some implementations, ratios between different vectorcomponent measurements from different vehicle transmit antennas can bedetermined, such as VxAn/VyAn, VxAn/VzAn, VyAn/VzAn. The ratios can beextended to any number of vehicle transmit antennas.

FIG. 3 illustrates a hardware system 300 including comparators fordetecting phase (sign) information between two channels according tosome embodiments. In some implementations, system 300 can includeamplifier chain 301, digital RSSI control comparator 304, channelcomparators 305 a-305 c and logic gates 306 a-306 c. Amplifier chain 101further includes adjustable gain amplifiers 302 a, 302 b and buffer 303.In the example shown, the x channel is coupled to an output ofadjustable gain amplifier 302 b. The output of buffer 303 is coupled toan input of digital RSSI control comparator 304, where it is compared toa comparator threshold value Vth to generate a digital RSSI controlsignal. The RSSI control signal is processed in a way to control theamplifier chain 301 to set the peak value of the if_amp_x signal to Vth.The RSSI control mechanism is shown here only for channel x, but it isimplemented also for channel y and channel z. Although not shown in thisexample, the y and z channels are also coupled to amplifiers inamplifier chain 301.

In this example implementation, the amplifier output signals arecompared at 70.7% of their peak voltage by channel comparators 305 a-305c while the peak value of all channels is equal due to the RSSI controlmechanism. The comparator output signals of the individual channels havea duty cycle of 25% (90° of 360°) and are compared to each other bylogic gates 306 a-306 c, which in this example are implemented as ANDfunctions (e.g., AND gates) as follows:x is compared to y>output signal-->sign x, y;x is compared to z>output signal-->sign x, z; andy is compared to z>output signal-->sign y, z.

Outputs are generated by AND gates 306 a-306 c when two comparatoroutput signals are present at the same time, thereby indicating that thetwo channels being compared are in-phase. If two channels are in-phasethey have the same polarity, being out-of-phase indicates that they haveopposite polarity.

Returning to the previous example described in reference to FIGS. 1, 2Aand 2B, the 8 possible vector

interpretations without sign detection are: (1, 4, 2), (1, 4, −2), (1,−4, −2), (−1, 4, −2), (−1, 4, 2), (−1, 4, −2), (−1, −4, 2) and (−1, −4,−2). Using the sign detection process implemented by system 300 andnoting that channels x and y (FIG. 2A) are in-phase and channels x and zare not in-phase (FIG. 2B), the 8 possible vector

interpretations are reduced to two vector

interpretations: (1, 4, −2) and (−1, −4, 2). This example reduction invector interpretations was accomplished by detecting via the signdetection mechanism that channel x has the same polarity as channel yand channel z has opposite polarity in respect to channel x. The onlyvector interpretations in the example set of 8 vector interpretationsthat meet this reduction criterion are: (1, 4, −2) and (−1, −4, 2).

Likewise, the possible vector

interpretations without sign detection are: (3, 3, 1), (3, 3, −1), (3,−3, 1), (3, −3, −1), (−3, 3, 1), (−3, 3, −1), (−3, −3, 1) and (−3, −3,−1). Using the sign detection process implemented by system 300, the 8possible vector

interpretations are reduced to two vector

interpretations: (−3, 3, 1) and (3, −3, −1). With sign detectionimplemented,

·

results in 2*2=4 possible vector interpretations, which in this exampleare [7, −7, −7, 7]. The angle calculation of Equation [2] results in[69.5, 110.5, 110.5, 69.5], which means that only two different angles[69.6, 110.5] need to be evaluated for relay attack prevention in a PEPSsystem.

FIG. 4 is a conceptual block diagram illustrating components used in asystem 400 for secure contactless data communication that implementssign detection in multi-dimensional signal measurements, as described inreference to FIGS. 1-3. In some embodiments, system 400 includestransceiver SE1 and transceiver SE2. In some embodiments, a dataexchange or communication may occur by transmitting a data carryingmodulated electromagnetic field between the transceiver SE1 andtransceiver SE2. The transceiver SE1 comprises a control unit CU. Thecontrol unit CU is coupled to a first output driver OD1 and to a secondoutput driver OD2. A first transmitting antenna SA1 is coupled to thefirst output driver OD1 and a second transmitting antenna SA2 is coupledto the second output driver OD2. In some implementations, SE2 can beincluded in, for example, a key or key fob used with PEPS system and SE1can be included in a vehicle, where SA1 and SA2 are vehicle antennas.

In some embodiments, transceiver SE2 comprises three antennas EA1, EA2and EA3 that are oriented orthogonally relative to each other. Receivingantennas EA1, EA2 and EA3 are coupled to signal amplifiers V1, V2 andV3, respectively. Signal amplifiers V1, V2 and V3 are coupled to inputsEAD1, EAD2 and EAD3 of an analog-to-digital (A/D) converter AD1,respectively. Furthermore, each input EAD1, EAD2 and EAD3 of the A/Dconverter AD1 is coupled with input ED1, ED2 and ED3 of a demodulatorDEM, respectively. In this manner, the signal received by each one ofthe receiving antennas EA1, EA2 and EA3 can be individually demodulatedto obtain and evaluate the data being carried by the modulated signal asreceived by each of the receiving antennas. The A/D converter AD1 andthe demodulator DEM are also each respectively coupled with a signalprocessor SP, which in turn is further coupled with a memory unit MEM.In some embodiments, elements similar to A/D converter AD1, demodulatorDEM, signal processor SP and memory unit MEM may be included intransceiver SE1.

In some embodiments, signal processor SP includes hardware for executinginstructions, such as those making up a computer program. As an exampleand not by way of limitation, to execute instructions, signal processorSP may retrieve (or fetch) the instructions from an internal register,an internal cache, memory unit MEM, or storage; decode and execute them;and then write one or more results to an internal register, an internalcache, memory unit MEM, or storage. In particular embodiments, signalprocessor SP may include one or more internal caches for data,instructions, or addresses. This disclosure contemplates signalprocessor SP including any suitable number of any suitable internalcaches, where appropriate.

This disclosure contemplates one or more computer-readable storage mediaimplementing any suitable storage. In particular embodiments, acomputer-readable storage medium implements one or more portions ofsignal processor SP (such as, for example, one or more internalregisters or caches), one or more portions of memory unit MEM, or acombination of these, where appropriate. In particular embodiments, acomputer-readable storage medium implements RAM or ROM. In particularembodiments, a computer-readable storage medium implements volatile orpersistent memory. In particular embodiments, one or morecomputer-readable storage media embody software. Herein, reference tosoftware may encompass one or more applications, byte code, one or morecomputer programs, one or more executable, one or more instructions,logic, machine code, one or more scripts, or source code, and viceversa, where appropriate. In particular embodiments, software includesone or more application programming interfaces (APIs). This disclosurecontemplates any suitable software written or otherwise expressed in anysuitable programming language or combination of programming languages.In particular embodiments, software is expressed as source code orobject code. In particular embodiments, software is expressed in ahigher-level programming language, such as, for example, C, Perl, or asuitable extension thereof. In particular embodiments, software isexpressed in a lower-level programming language, such as assemblylanguage, machine code, or hardware description language.

FIG. 5 is a flow diagram of a process 500 of sign detection inmulti-dimensional signal measurements. Process 500 can be implementedby, for example, one or more components of system 400, described inreference to FIG. 4. In some implementations, part or all of process 500can be implemented as instructions stored on a non-transitorycomputer-readable storage medium and executed by one or more processorsor processing cores, such as SP, described in reference to system 400.

In some implementations, process 500 can begin by receiving orthogonalchannel signals (502). For example, the signals can be analog signalsreceived from 3 orthogonally oriented antennas that are converted (e.g.,AD1) to digital signals that can be processed by digital processor(e.g., SP).

Process 500 can continue by measuring the channel signals includingdetermining sign information (504). For example, the channel signals canbe inputs to comparator functions to determine if the channels are inphase (same sign or polarity) or out of phase (different sign orpolarity), where each channel represents a vector component of areceived magnetic field. The comparing function can be implemented inhardware (FIG. 3) or software by a signal processor (FIG. 4) or acombination of both hardware and software components.

Process 500 can continue by reducing the possible number of vectorinterpretations based on the sign information (506). For example, if thex and y channels have the same signs (same polarity) and the x and zchannel signals have different signs (different polarity), than thevector interpretations that have different signs for the x and ychannels or the same sign for the x and z channels are excluded fromfurther processing for angle or angle difference evaluations or vectorcomponent ratios.

Process 500 can continue by detecting a relay attack based on thereduced set of vector determinations (508). For example, the reducedvector interpretations determined in step 506 can be used to generate aset of angles or angle differences or vector component ratios betweenthe reduced set of vectors, which can be compared (together with theRSSI value) with a predetermined or expected set of angles or angledifferences or vector component ratios to determine if the expectedcriteria to detect a relay attack situation are met. If these criteriaare met (within a certain tolerance range), the key or key fob will nottransmit an authentication code to the vehicle, thereby preventing relayattacks.

Although in example step 508 the reduced possible number of magneticvector interpretations is used to detect relay attacks against, forexample, a PEPS system, process 500 can also be applied to anyapplication that could benefit from reducing a possible number of vectorinterpretations in a vector space and thus should not be construed to belimited to magnetic field vectors or detecting relay attacks.

While this document contains many specific implementation details, theseshould not be construed as limitations on the scope what may be claimed,but rather as descriptions of features that may be specific toparticular embodiments. Certain features that are described in thisspecification in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable sub combination. Moreover, although features may be describedabove as acting in certain combinations and even initially claimed assuch, one or more features from a claimed combination can, in somecases, be excised from the combination, and the claimed combination maybe directed to a sub combination or variation of a sub combination.

What is claimed is:
 1. A system comprising: an interface operable toobtain signals from antennas, where the signals correspond to componentsof vectors in space; one or more signal processors coupled to theinterface and configured to: determine polarities of the signals basedon phase measurements between the signals; reduce a possible number ofvector interpretations based on the determined polarities of thesignals; reduce a possible number of angles or angle differences betweenthe vectors based on the reduced possible number of vectorinterpretations; and compare the reduced possible number of angles orangle differences to predetermined angle or angle differences.
 2. Thesystem of claim 1, where comparing the polarities of the signalsincludes comparing the signals with threshold values.
 3. The system ofclaim 2, where the threshold values are a percentage of maximum valuesof the signals.
 4. The system of claim 1, where the interface comprises:one or more signal amplifiers configured to amplify the signals; one ormore analog-to-digital converters (ADCs) coupled to the signalamplifiers and configured to convert the amplified signals to digitalvalues; and the one or more signal processors coupled to the one or moreADCs and configured for determining the polarities of the signals basedon the digital values.
 5. The system of claim 3, further comprising: oneor more signal amplifiers configured to amplify the signals; comparatorshaving inputs coupled to outputs of the signal amplifiers and thethreshold voltages, the comparators configured for indicating when thesignals exceed the threshold values; and logic configured to comparecomparator outputs to determine the polarities of the signals.
 6. Thesystem of claim 1, where one or more ratios between the components ofone or more vectors are determined based on the reduced possible numberof vector interpretations; and the one or more actions related to thesystem are performed based on comparison of the ratios with expectedratios.
 7. The system of claim 6, where the ratios are determined forsame vector component for two different vectors.
 8. The system of claim6, where the ratios are determined for different vector components fortwo different vectors.
 9. The system of claim 1, where the circuit isincluded in a key or key fob of a passive entry, passive start (PEPS)system of a vehicle.
 10. The system of claim 1, where the possiblenumber of vector interpretations is reduced from eight to two.
 11. Amethod comprising: obtaining, by an interface of a system, signals fromantennas coupled to the interface, where the signals correspond tocomponents of vectors in space; determining, by one or more signalprocessors of the system, polarities of the signals based on phasemeasurements between the signals; reducing, by the one or more signalprocessors, a possible number of vector interpretations based on thedetermined polarities of the signals; reducing, by the one or moresignal processors, a possible number of angles or angle differencesbetween the vectors based on the reduced possible number of vectorinterpretations; and comparing, by the one or more signal processors,the reduced possible number of angles or angle differences topredetermined angles or angle differences.
 12. The method of claim 11,where comparing the polarities of the signals includes comparing thesignals with threshold values.
 13. The method of claim 12, where thethreshold values are a percentage of maximum values of the signals. 14.The method of claim 11, further comprising: amplifying the signals byone or more signal amplifiers coupled to the interface; converting theamplified signals to digital values by one or more analog-to-digitalconverters (ADCs) coupled to the signal amplifiers; and determining, bythe one or more signal processors coupled to the one or more ADCs, thepolarities of the signals based on the digital values.
 15. The method ofclaim 12, further comprising: amplifying the signals by one or moresignal amplifiers coupled to the interface; comparing the signals withthreshold voltages, by comparators having inputs coupled to outputs ofthe signal amplifiers and the threshold voltages, to indicate when thesignals exceed the threshold values; and comparing, by logic, comparatoroutputs to determine polarities of the signals.
 16. The method of claim11, further comprising: determining one or more ratios between thecomponents of one or more vectors based on the reduced possible numberof vector interpretations; and performing one or more actions related tothe system based on comparison of the ratios with expected ratios. 17.The method of claim 16, where the ratios are determined for same vectorcomponent for two different vectors.
 18. The method of claim 16, wherethe ratios are determined for different vector components for twodifferent vectors.
 19. A non-transitory, computer-readable storagemedium having instructions stored thereon, which, when executed by oneor more processors, causes the one or more processors to performoperations comprising: obtaining antenna signals that correspond tocomponents of vectors in space; determining polarities of the signalsbased on phase measurements between the signals; reducing a possiblenumber of vector interpretations based on the determined polarities ofthe signals; reducing a possible number of angles or angle differencesbetween the vectors based on the reduced possible number of vectorinterpretations; and comparing the reduced possible number of angles orangle differences to predetermined angles or angle differences.
 20. Thenon-transitory, computer-readable storage medium of claim 19, wherecomparing the signs or polarities of the signals includes comparing thesignals with threshold values.